What is the value of sin(arctan(-(sqrt(3))/3)) ?

The value of sin(arctan(-(sqrt(3))/3)) is -1/2

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sin(arctan(-(sqrt(3))/3))

sin (arctan (- \frac{3}{3}))

- \frac{1}{2}

Decimal Notation

- 0.5

Solution steps

sin (arctan (- \frac{3}{3}))

Rewrite using trig identities:

sin (arctan (- \frac{3}{3})) = \frac{( - \frac{3}{3} ) 1 + ( - \frac{3}{3} ) ^{2}}{1 + ( - \frac{3}{3} ) ^{2}}

Use the following identity:

sin (arctan (x)) = \frac{x 1 + x ^{2}}{1 + x ^{2}}

= \frac{( - \frac{3}{3} ) 1 + ( - \frac{3}{3} ) ^{2}}{1 + ( - \frac{3}{3} ) ^{2}}

= \frac{( - \frac{3}{3} ) 1 + ( - \frac{3}{3} ) ^{2}}{1 + ( - \frac{3}{3} ) ^{2}}

Simplify

= - \frac{1}{2}

sec (- \frac{4 π}{3})

csc (- 3 0^{\circ})

arccos (cos (\frac{π}{3}))

cos (4 5^{\circ}) cos (1 5^{\circ})

tan (- 16 5^{\circ})

What is the value of sin(arctan(-(sqrt(3))/3)) ?
The value of sin(arctan(-(sqrt(3))/3)) is -1/2